Artificial compressibility method for high-pressure transcritical fluids at low Mach numbers

Supercritical fluids possess unique properties that makes them relevant in various scientific and engineering applications. However, the experimental investigation of these fluids is challenging due to the high pressures involved and their complex thermophysical behavior. To overcome these limitations, computational researchers employ scale-resolving methods, such as direct numerical simulation and large-eddy simulation to study them. Nonetheless, these methods require substantial computational resources, especially in the case of low-Mach-number regimes due to the disparity between acoustic and hydrodynamic/thermal time scales. This work, therefore, addresses this problem by extending the artificial compressibility method to high-pressure transcritical fluids. This method is based on decoupling the thermodynamic and hydrodynamic parts of the pressure field, such that the acoustic time scales can be externally modified without severely impacting the flow physics of the problem. In addition, the method proposed has two key characteristics: (i) the splitting method presents low computational complexity, and (ii) an automatic strategy for selecting the speedup factor of the approach is introduced. The effectiveness of the resulting methodology is demonstrated through comprehensive numerical tests of increasing complexity, showcasing its ability to accurately simulate a wide range of high-pressure transcritical flows including turbulence. The results obtained indicate that the approach proposed can readily lead to computational speedups larger than 10x without significantly compromising the accuracy of the numerical solutions.